In many collation algorithms, the comparison is based not on the numerical codes of the characters, but with reference to the collating sequence – a sequence in which the characters are assumed to come for the purpose of collation – as well as other ordering rules appropriate to the given application.

In physical sciences, numerical values ( such as constants, quantities, or scales of measurement ) are called conventional if they do not represent a measured property of nature, but originate in a convention, for example an average of many measurements, agreed between the scientists working with these values.

Fourier analysis has many scientific applications – in physics, partial differential equations, number theory, combinatorics, signal processing, imaging, probability theory, statistics, option pricing, cryptography, numerical analysis, acoustics, oceanography, sonar, optics, diffraction, geometry, protein structure analysis and other areas.

There are many numerology systems which assign numerical value to the letters of an alphabet.

The field of numerical analysis predates the invention of modern computers by many centuries.

Under this narrower definition, which differs from that historically used by many ( though by no means all ) Christians and other Westerners, contemporary Paganism is a smaller and more marginal numerical phenomenon.

For a great many functions and practical applications, the Riemann integral can also be readily evaluated by using the fundamental theorem of calculus or ( approximately ) by numerical integration.

Separability is especially important in numerical analysis and constructive mathematics, since many theorems that can be proved for nonseparable spaces have constructive proofs only for separable spaces.

In computer science, zero is thus often used as the base case for many kinds of numerical recursion.

The monograph Orthogonal polynomials, published in 1939, contains much of his research and has had a profound influence in many areas of applied mathematics, including theoretical physics, stochastic processes and numerical analysis.

After two days of defending against an enemy with an overwhelming numerical superiority, enduring heavy artillery fire and aerial bombardment, and with many of his troops in open flight, it became obvious to Tang that a general retreat was inevitable.

Because floating point versions of orthogonal matrices have advantageous properties, they are key to many algorithms in numerical linear algebra, such as QR decomposition.

Numerical analysis takes advantage of many of the properties of orthogonal matrices for numerical linear algebra, and they arise naturally.

In many numerical models and observational syntheses, the Southern Ocean upwelling represents the primary means by which deep dense water is brought to the surface.

As these topics are explored, many more general numerical and mathematical problems are encountered in the process of calculating physical properties of the modeled systems.

He advanced the science of cranial anthropometry by developing many new types of measuring instruments ( craniometers ) and numerical indices.

By utilizing matrix-based computation, dynamic typing, and automatic memory management, many numerical problems may be expressed in a reduced number of code lines, as compared to similar solutions using traditional languages, such as Fortran, C, or C ++.

The speed of the attack ( which was not preceded by artillery fire ) and the numerical superiority concentrated on a single point, disrupted and demoralized the defenders, putting them to flight, retreating, without many casualties.

Unfortunately, many numerical optimization techniques, such as hill climbing, gradient descent, some of the quasi-Newton methods, among others, are designed to find local maxima ( or minima ) and not saddle points.

The output from the CAM software is usually a simple text file of G-code, sometimes many thousands of commands long, that is then transferred to a machine tool using a direct numerical control ( DNC ) program.

For modeling of scattering in cases where the Rayleigh and Mie models do not apply such as irregularly shaped particles, there are many numerical methods that can be used.

He taught and solved problems from many fields: the usage of mathematics in natural and social sciences, statistics, mechanics, classical applied mathematics, discrete mathematics, graph and network theory, linear programming, operational researches, numerical analysis.

The acceleration () caused by the thruster force is just an additional acceleration to be added to the other accelerations ( force per unit mass ) affecting the spacecraft and the orbit can easily be propagated with a numerical algorithm including also this thruster force .< ref > The thrust force per unit mass being where and are given functions of time But for many purposes, typically for studies or for maneuver optimization, they are approximated by impulsive maneuvers as illustrated in figure 1 with a as given by ().

For example, the iPhone ( which by its name implies that its primary function is that of a mobile phone ) can perform many different tasks, but does not feature a traditional numerical pad to make phone calls.

It forms the core of many, perhaps most, problems of psychotherapy.

Such study may take many forms.

This understanding, of course, may in its turn take many forms and some of these -- especially those most interesting to the student of comparative literature -- are essentially historical.

Open societies can take many forms, and within very broad limits recipients must be free to set their own goals and to devise their own institutions to achieve those goals.

The importance of knowing in what chemical forms the hormone may exist is accentuated by the recent observation that there exists an abnormally long-acting TSH in blood drawn from many thyrotoxic patients ( Adams, 1958 ).

We spend billions of dollars on liquor, and many more billions on various forms of escapist entertainment.

The anti-slavery movement took many forms.

It takes many forms, this prayer, but in essence it is always a request for guidance, for open minds and gentle hearts, for honesty and sincerity, for the wisdom and the insights that will help Guideposts' readers.

The Pittosporaceae were placed within the Rosales, and many of the other forms within the family Cornaceae.

Warhol's artwork ranged in many forms of media that include hand drawing, painting, printmaking, photography, silk screening, sculpture, film, and music.

In the Middle East, Aramaic gave rise to the Hebrew and Nabataean abjads, which retained many of the Aramaic letter forms.

Beginning with Reginald Fessenden's audio demonstrations in 1906, it was also the original method used for audio radio transmissions, and remains in use today by many forms of communication —" AM " is often used to refer to the mediumwave broadcast band ( see AM radio ).

Many religions, whether they believe in the soul's existence in another world like Christianity, Islam and many pagan belief systems, or in reincarnation like many forms of Hinduism and Buddhism, believe that one's status in the afterlife is a reward or punishment for their conduct during life.

Because they often exhibit a combination of high strength and low weight, these alloys became widely used in many forms of industry, including the construction of modern aircraft.

In solids, mechanical waves can take many forms including longitudinal waves, transverse waves and surface waves.

There are typically three mathematical forms for the radial functions R ( r ) which can be chosen as a starting point for the calculation of the properties of atoms and molecules with many electrons.

Without a writing system, the Ainu were masters of narration, with the Yukar and other forms of narration such as the Uepeker ( Uwepeker ) tales, being committed to memory and related at gatherings, often lasting many hours or even days.

Aalto claimed that his paintings were not made as individual artworks but as part of his process of architectural design, and many of his small-scale " sculptural " experiments with wood led to later larger architectural details and forms.

For instance member nations of the Commonwealth where English is not spoken natively, such as India, often closely follow British English forms, while many American English usages are followed in other countries which have been historically influenced by the United States, such as the Philippines.

African art existed in many forms and styles, and with fairly little influence from outside Africa.

Abiotic stress comes in many forms.

Target acquisition can take many forms, it is usually observation in real time but may be the product of analysis.

Moreover they argued that some species have been created for the purpose of being sacrificed and eaten by humans, that it is normal for animals to kill and eat other animals, that agriculture, too, inevitably leads to the death of many animals, that plants are living beings as well and must still be destroyed, that we unintentionally and unknowingly destroy life forms all the time, and that a hunted animal has a fair chance to survive by killing the hunter.

In many cases, the people he conquered had rebelled against their Islamic overloards and reverted to prior forms of worship.